Bad Directions in Cryptographic Hash Functions

A 25-gigabyte "point obfuscation" challenge "using security parameter 60" was announced at the Crypto 2015 rump session; "point obfuscation" is another name for password hashing. This paper shows that the particular matrix-multiplication hash function used in the challenge is much less secure than previous password-hashing functions are believed to be. This paper's attack algorithm broke the challenge in just 19 minutes using a cluster of 21 PCs. Keywords: symmetric cryptography, hash functions, password hashing, point obfuscation, matrix multiplication, meet-in-the-middle attacks, meet-in-many-middles attack

Bad directions in cryptographic hash functions

A 25-gigabyte point obfuscation challenge using security parameter 60 was announced at the Crypto 2015 rump session; point obfuscation is another name for password hashing. This paper shows that the particular matrix-multiplication hash function used in the challenge is much less secure than previous password-hashing functions are believed to be. This paper\u27s attack algorithm broke the challenge in just 19 minutes using a cluster of 21 PCs

Catena: A Memory-Consuming Password-Scrambling Framework

It is a common wisdom that servers should store the one-way hash of their clients’ passwords, rather than storing the password in the clear. In this paper we introduce a set of functional properties a key-derivation function (password scrambler) should have. Unfortunately, none of the existing algorithms satisfies our requirements and therefore, we introduce a novel and provably secure password scrambling framework (PSF) called Catena. Furthermore, we introduce two instantiations of Catena based on a memory-consuming one-way functions. Thus, Catena excellently thwarts massively parallel attacks on cheap memory-constrained hardware, such as recent graphical processing units (GPUs). Additionally, we show that Catena is also a good key-derivation function, since – in the random oracle model – it is indistinguishable from a random function. Furthermore, the memory-access pattern of both instantiations is password-independent and therefore, Catena provides resistance against cache-timing attacks. Moreover, Catena is the first PSF which naturally supports (1) client-independent updates (the server can increase the security parameters and update the password hash without user interaction or knowing the password), (2) an optional server relief protocol (saving the server’s resources at the cost of the client), and (3) a variant Catena-KG for secure key derivation (to securely generate many cryptographic keys of arbitrary lengths such that compromising some keys does not help to break others). We denote a password scrambler as a PSF with a certain instantiation

Hardware Implementations of a Variant of the Zémor-Tillich Hash Function: Can a Provably Secure Hash Function be very efficient ?

Hash functions are widely used in Cryptography, and hardware implementations of hash functions are of interest in a variety of contexts such as speeding up the computations of a network server or providing authentication in small electronic devices such as RFID tags. Provably secure hash functions, the security of which relies on the hardness of a mathematical problem, are particularly appealing for security, but they used to be too inefficient in practice. In this paper, we study the efficiency in hardware of ZT\u27, a provably secure hash function based on the Zémor-Tillich hash function. We consider three kinds of implementations targeting a high throughput and a low area in different ways. We first present a high-speed implementation of ZT\u27 on FPGA that is nearly half as efficient as state-of-the-art SHA implementations in terms of throughput per area. We then focus on area reduction and present an ASIC implementation of ZT\u27 with much smaller area costs than SHA-1 and even than SQUASH, which was specially designed for low-cost RFID tags. Between these two extreme implementations, we show that the throughput and area can be traded with a lot of flexibility. Finally, we show that the inherent parallelism of ZT\u27 makes it particularly suitable for applications requiring high speed hashing of very long messages. Our work, together with existing reasonably efficient software implementations, shows that this variant of the Zémor-Tillich hash function is in fact very practical for a wide range of applications, while having a security related to the hardness of a mathematical problem and significant additional advantages such as scalability and parallelism

Cayley hashing with cookies

Cayley hash functions are based on a simple idea of using a pair of semigroup elements, $A$ and $B$, to hash the 0 and 1 bit, respectively, and then to hash an arbitrary bit string in the natural way, by using multiplication of elements in the semigroup. The main advantage of Cayley hash functions compared to, say, hash functions in the SHA family is that when an already hashed document is amended, one does not have to hash the whole amended document all over again, but rather hash just the amended part and then multiply the result by the hash of the original document. Some authors argued that this may be a security hazard, specifically that this property may facilitate finding a second preimage by splitting a long bit string into shorter pieces. In this paper, we offer a way to get rid of this alleged disadvantage and keep the advantages at the same time. We call this method ``Cayley hashing with cookies using terminology borrowed from the theory of random walks in a random environment. For the platform semigroup, we use $2\times 2$ matrices over $F_p$

Design and Analysis of Cryptographic Algorithms for Authentication

During the previous decades, the upcoming demand for security in the digital world, e.g., the Internet, lead to numerous groundbreaking research topics in the field of cryptography. This thesis focuses on the design and analysis of cryptographic primitives and schemes to be used for authentication of data and communication endpoints, i.e., users. It is structured into three parts, where we present the first freely scalable multi-block-length block-cipher-based compression function (Counter-bDM) in the first part. The presented design is accompanied by a thorough security analysis regarding its preimage and collision security. The second and major part is devoted to password hashing. It is motivated by the large amount of leaked password during the last years and our discovery of side-channel attacks on scrypt – the first modern password scrambler that allowed to parameterize the amount of memory required to compute a password hash. After summarizing which properties we expect from a modern password scrambler, we (1) describe a cache-timing attack on scrypt based on its password-dependent memory-access pattern and (2) outline an additional attack vector – garbage-collector attacks – that exploits optimization which may disregard to overwrite the internally used memory. Based on our observations, we introduce Catena – the first memory-demanding password-scrambling framework that allows a password-independent memory-access pattern for resistance to the aforementioned attacks. Catena was submitted to the Password Hashing Competition (PHC) and, after two years of rigorous analysis, ended up as a finalist gaining special recognition for its agile framework approach and side-channel resistance. We provide six instances of Catena suitable for a variety of applications. We close the second part of this thesis with an overview of modern password scramblers regarding their functional, security, and general properties; supported by a brief analysis of their resistance to garbage-collector attacks. The third part of this thesis is dedicated to the integrity (authenticity of data) of nonce-based authenticated encryption schemes (NAE). We introduce the so-called j-IV-Collision Attack, allowing to obtain an upper bound for an adversary that is provided with a first successful forgery and tries to efficiently compute j additional forgeries for a particular NAE scheme (in short: reforgeability). Additionally, we introduce the corresponding security notion j-INT-CTXT and provide a comparative analysis (regarding j-INT-CTXT security) of the third-round submission to the CAESAR competition and the four classical and widely used NAE schemes CWC, CCM, EAX, and GCM.Die fortschreitende Digitalisierung in den letzten Jahrzehnten hat dazu geführt, dass sich das Forschungsfeld der Kryptographie bedeutsam weiterentwickelt hat. Diese, im Wesentlichen aus drei Teilen bestehende Dissertation, widmet sich dem Design und der Analyse von kryptographischen Primitiven und Modi zur Authentifizierung von Daten und Kommunikationspartnern. Der erste Teil beschäftigt sich dabei mit blockchiffrenbasierten Kompressionsfunktionen, die in ressourcenbeschränkten Anwendungsbereichen eine wichtige Rolle spielen. Im Rahmen dieser Arbeit präsentieren wir die erste frei skalierbare und sichere blockchiffrenbasierte Kompressionsfunktion Counter-bDM und erweitern somit flexibel die erreichbare Sicherheit solcher Konstruktionen. Der zweite Teil und wichtigste Teil dieser Dissertation widmet sich Passwort-Hashing-Verfahren. Zum einen ist dieser motiviert durch die große Anzahl von Angriffen auf Passwortdatenbanken großer Internet-Unternehmen. Zum anderen bot die Password Hashing Competition (PHC) die Möglichkeit, unter Aufmerksamkeit der Expertengemeinschaft die Sicherheit bestehender Verfahren zu hinterfragen, sowie neue sichere Verfahren zu entwerfen. Im Rahmen des zweiten Teils entwarfen wir Anforderungen an moderne Passwort-Hashing-Verfahren und beschreiben drei Arten von Seitenkanal-Angriffen (Cache-Timing-, Weak Garbage-Collector- und Garbage-Collector-Angriffe) auf scrypt – das erste moderne Password-Hashing-Verfahren welches erlaubte, den benötigten Speicheraufwand zur Berechnung eines Passworthashes frei zu wählen. Basierend auf unseren Beobachtungen und Angriffen, stellen wir das erste moderne PasswordHashing-Framework Catena vor, welches für gewählte Instanzen passwortunabhängige Speicherzugriffe und somit Sicherheit gegen oben genannte Angriffe garantiert. Catena erlangte im Rahmen des PHC-Wettbewerbs besondere Anerkennung für seine Agilität und Resistenz gegen SeitenkanalAngriffe. Wir präsentieren sechs Instanzen des Frameworks, welche für eine Vielzahl von Anwendungen geeignet sind. Abgerundet wird der zweite Teil dieser Arbeit mit einem vergleichenden Überblick von modernen Passwort-Hashing-Verfahren hinsichtlich ihrer funktionalen, sicherheitstechnischen und allgemeinen Eigenschaften. Dieser Vergleich wird unterstützt durch eine kurze Analyse bezüglich ihrer Resistenz gegen (Weak) Garbage-Collector-Angriffe. Der dritte teil dieser Arbeit widmet sich der Integrität von Daten, genauer, der Sicherheit sogenannter Nonce-basierten authentisierten Verschlüsselungsverfahren (NAE-Verfahren), welche ebenso wie Passwort-Hashing-Verfahren in der heutigen Sicherheitsinfrastruktur des Internets eine wichtige Rolle spielen. Während Standard-Definitionen keine Sicherheit nach dem Fund einer ersten erfolgreich gefälschten Nachricht betrachten, erweitern wir die Sicherheitsanforderungen dahingehend wie schwer es ist, weitere Fälschungen zu ermitteln. Wir abstrahieren die Funktionsweise von NAEVerfahren in Klassen, analysieren diese systematisch und klassifizieren die Dritt-Runden-Kandidaten des CAESAR-Wettbewerbs, sowie vier weit verbreitete NAE-Verfahren CWC, CCM, EAX und GCM

Cayley Graphs of Semigroups and Applications to Hashing

In 1994, Tillich and Zemor proposed a scheme for a family of hash functions that uses products of matrices in groups of the form $SL_2(F_{2^n})$. In 2009, Grassl et al. developed an attack to obtain collisions for palindromic bit strings by exploring a connection between the Tillich-Zemor functions and maximal length chains in the Euclidean algorithm for polynomials over $F_2$. In this work, we present a new proposal for hash functions based on Cayley graphs of semigroups. In our proposed hash function, the noncommutative semigroup of linear functions under composition is considered as platform for the scheme. We will also discuss its efficiency, pseudorandomness and security features. Furthermore, we generalized the Fit-Florea and Matula\u27s algorithm (2004) that finds the discrete logarithm in the multiplicative group of integers modulo $2^k$ by establishing a connection between semi-primitive roots modulo $2^k$ where $k\geq 3$ and the logarithmic base used in the algorithm

Design and Analysis of Cryptographic Algorithms for Authentication

During the previous decades, the upcoming demand for security in the digital world, e.g., the Internet, lead to numerous groundbreaking research topics in the field of cryptography. This thesis focuses on the design and analysis of cryptographic primitives and schemes to be used for authentication of data and communication endpoints, i.e., users. It is structured into three parts, where we present the first freely scalable multi-block-length block-cipher-based compression function (Counter-bDM) in the first part. The presented design is accompanied by a thorough security analysis regarding its preimage and collision security. The second and major part is devoted to password hashing. It is motivated by the large amount of leaked password during the last years and our discovery of side-channel attacks on scrypt – the first modern password scrambler that allowed to parameterize the amount of memory required to compute a password hash. After summarizing which properties we expect from a modern password scrambler, we (1) describe a cache-timing attack on scrypt based on its password-dependent memory-access pattern and (2) outline an additional attack vector – garbage-collector attacks – that exploits optimization which may disregard to overwrite the internally used memory. Based on our observations, we introduce Catena – the first memory-demanding password-scrambling framework that allows a password-independent memory-access pattern for resistance to the aforementioned attacks. Catena was submitted to the Password Hashing Competition (PHC) and, after two years of rigorous analysis, ended up as a finalist gaining special recognition for its agile framework approach and side-channel resistance. We provide six instances of Catena suitable for a variety of applications. We close the second part of this thesis with an overview of modern password scramblers regarding their functional, security, and general properties; supported by a brief analysis of their resistance to garbage-collector attacks. The third part of this thesis is dedicated to the integrity (authenticity of data) of nonce-based authenticated encryption schemes (NAE). We introduce the so-called j-IV-Collision Attack, allowing to obtain an upper bound for an adversary that is provided with a first successful forgery and tries to efficiently compute j additional forgeries for a particular NAE scheme (in short: reforgeability). Additionally, we introduce the corresponding security notion j-INT-CTXT and provide a comparative analysis (regarding j-INT-CTXT security) of the third-round submission to the CAESAR competition and the four classical and widely used NAE schemes CWC, CCM, EAX, and GCM.Die fortschreitende Digitalisierung in den letzten Jahrzehnten hat dazu geführt, dass sich das Forschungsfeld der Kryptographie bedeutsam weiterentwickelt hat. Diese, im Wesentlichen aus drei Teilen bestehende Dissertation, widmet sich dem Design und der Analyse von kryptographischen Primitiven und Modi zur Authentifizierung von Daten und Kommunikationspartnern. Der erste Teil beschäftigt sich dabei mit blockchiffrenbasierten Kompressionsfunktionen, die in ressourcenbeschränkten Anwendungsbereichen eine wichtige Rolle spielen. Im Rahmen dieser Arbeit präsentieren wir die erste frei skalierbare und sichere blockchiffrenbasierte Kompressionsfunktion Counter-bDM und erweitern somit flexibel die erreichbare Sicherheit solcher Konstruktionen. Der zweite Teil und wichtigste Teil dieser Dissertation widmet sich Passwort-Hashing-Verfahren. Zum einen ist dieser motiviert durch die große Anzahl von Angriffen auf Passwortdatenbanken großer Internet-Unternehmen. Zum anderen bot die Password Hashing Competition (PHC) die Möglichkeit, unter Aufmerksamkeit der Expertengemeinschaft die Sicherheit bestehender Verfahren zu hinterfragen, sowie neue sichere Verfahren zu entwerfen. Im Rahmen des zweiten Teils entwarfen wir Anforderungen an moderne Passwort-Hashing-Verfahren und beschreiben drei Arten von Seitenkanal-Angriffen (Cache-Timing-, Weak Garbage-Collector- und Garbage-Collector-Angriffe) auf scrypt – das erste moderne Password-Hashing-Verfahren welches erlaubte, den benötigten Speicheraufwand zur Berechnung eines Passworthashes frei zu wählen. Basierend auf unseren Beobachtungen und Angriffen, stellen wir das erste moderne PasswordHashing-Framework Catena vor, welches für gewählte Instanzen passwortunabhängige Speicherzugriffe und somit Sicherheit gegen oben genannte Angriffe garantiert. Catena erlangte im Rahmen des PHC-Wettbewerbs besondere Anerkennung für seine Agilität und Resistenz gegen SeitenkanalAngriffe. Wir präsentieren sechs Instanzen des Frameworks, welche für eine Vielzahl von Anwendungen geeignet sind. Abgerundet wird der zweite Teil dieser Arbeit mit einem vergleichenden Überblick von modernen Passwort-Hashing-Verfahren hinsichtlich ihrer funktionalen, sicherheitstechnischen und allgemeinen Eigenschaften. Dieser Vergleich wird unterstützt durch eine kurze Analyse bezüglich ihrer Resistenz gegen (Weak) Garbage-Collector-Angriffe. Der dritte teil dieser Arbeit widmet sich der Integrität von Daten, genauer, der Sicherheit sogenannter Nonce-basierten authentisierten Verschlüsselungsverfahren (NAE-Verfahren), welche ebenso wie Passwort-Hashing-Verfahren in der heutigen Sicherheitsinfrastruktur des Internets eine wichtige Rolle spielen. Während Standard-Definitionen keine Sicherheit nach dem Fund einer ersten erfolgreich gefälschten Nachricht betrachten, erweitern wir die Sicherheitsanforderungen dahingehend wie schwer es ist, weitere Fälschungen zu ermitteln. Wir abstrahieren die Funktionsweise von NAEVerfahren in Klassen, analysieren diese systematisch und klassifizieren die Dritt-Runden-Kandidaten des CAESAR-Wettbewerbs, sowie vier weit verbreitete NAE-Verfahren CWC, CCM, EAX und GCM

Cryptographic Hash Functions in Groups and Provable Properties

We consider several "provably secure" hash functions that compute simple sums in a well chosen group (G,*). Security properties of such functions provably translate in a natural way to computational problems in G that are simple to define and possibly also hard to solve. Given k disjoint lists Li of group elements, the k-sum problem asks for gi ∊ Li such that g1 * g2 *...* gk = 1G. Hardness of the problem in the respective groups follows from some "standard" assumptions used in public-key cryptology such as hardness of integer factoring, discrete logarithms, lattice reduction and syndrome decoding. We point out evidence that the k-sum problem may even be harder than the above problems. Two hash functions based on the group k-sum problem, SWIFFTX and FSB, were submitted to NIST as candidates for the future SHA-3 standard. Both submissions were supported by some sort of a security proof. We show that the assessment of security levels provided in the proposals is not related to the proofs included. The main claims on security are supported exclusively by considerations about available attacks. By introducing "second-order" bounds on bounds on security, we expose the limits of such an approach to provable security. A problem with the way security is quantified does not necessarily mean a problem with security itself. Although FSB does have a history of failures, recent versions of the two above functions have resisted cryptanalytic efforts well. This evidence, as well as the several connections to more standard problems, suggests that the k-sum problem in some groups may be considered hard on its own, and possibly lead to provable bounds on security. Complexity of the non-trivial tree algorithm is becoming a standard tool for measuring the associated hardness. We propose modifications to the multiplicative Very Smooth Hash and derive security from multiplicative k-sums in contrast to the original reductions that related to factoring or discrete logarithms. Although the original reductions remain valid, we measure security in a new, more aggressive way. This allows us to relax the parameters and hash faster. We obtain a function that is only three times slower compared to SHA-256 and is estimated to offer at least equivalent collision resistance. The speed can be doubled by the use of a special modulus, such a modified function is supported exclusively by the hardness of multiplicative k-sums modulo a power of two. Our efforts culminate in a new multiplicative k-sum function in finite fields that further generalizes the design of Very Smooth Hash. In contrast to the previous variants, the memory requirements of the new function are negligible. The fastest instance of the function expected to offer 128-bit collision resistance runs at 24 cycles per byte on an Intel Core i7 processor and approaches the 17.4 figure of SHA-256. The new functions proposed in this thesis do not provably achieve a usual security property such as preimage or collision resistance from a well-established assumption. They do however enjoy unconditional provable separation of inputs that collide. Changes in input that are small with respect to a well defined measure never lead to identical output in the compression function

Analysis Design & Applications of Cryptographic Building Blocks

This thesis deals with the basic design and rigorous analysis of cryptographic schemes and primitives, especially of authenticated encryption schemes, hash functions, and password-hashing schemes. In the last decade, security issues such as the PS3 jailbreak demonstrate that common security notions are rather restrictive, and it seems that they do not model the real world adequately. As a result, in the first part of this work, we introduce a less restrictive security model that is closer to reality. In this model it turned out that existing (on-line) authenticated encryption schemes cannot longer beconsidered secure, i.e. they can guarantee neither data privacy nor data integrity. Therefore, we present two novel authenticated encryption scheme, namely COFFE and McOE, which are not only secure in the standard model but also reasonably secure in our generalized security model, i.e. both preserve full data inegrity. In addition, McOE preserves a resonable level of data privacy. The second part of this thesis starts with proposing the hash function Twister-Pi, a revised version of the accepted SHA-3 candidate Twister. We not only fixed all known security issues of Twister, but also increased the overall soundness of our hash-function design. Furthermore, we present some fundamental groundwork in the area of password-hashing schemes. This research was mainly inspired by the medial omnipresence of password-leakage incidences. We show that the password-hashing scheme scrypt is vulnerable against cache-timing attacks due to the existence of a password-dependent memory-access pattern. Finally, we introduce Catena the first password-hashing scheme that is both memory-consuming and resistant against cache-timing attacks